Demonstration of Coherent-State Discrimination Using a Displacement-Controlled Photon-Number-Resolving Detector

Abstract

We experimentally demonstrate a new measurement scheme for the discrimination of two coherent states. The measurement scheme is based on a displacement operation followed by a photon-number-resolving detector, and we show that it outperforms the standard homodyne detector which we, in addition, prove to be optimal within all Gaussian operations including conditional dynamics. We also show that the non-Gaussian detector is superior to the homodyne detector in a continuous variable quantum key distribution scheme.

Gaussian-only regenerative stations cannot act as quantum repeaters

“…Some examples are universal quantum computing [29], entanglement distillation of Gaussian states [30][31][32], optimal cloning of coherent states [33], optimal discrimination of coherent states [34][35][36][37], Gaussian quantum error correction [38], and building a jointdetection receiver for classical communication [39].…”

Optimally cloned binary coherent states

“…An intermediate regime where both erroneous and inconclusive results are allowed has also been considered [29] and the minimal probability of error for a fixed probability of inconclusive results has been derived for pure [51] and mixed states [52]. In the following, we always assume Comparison of the error probability of the homodyne detector (red, dotted), the Kennedy receiver (green, dashed) [24], the optimized displacement receiver (purple, dash-dotted) [29], and the Helstrom bound [20,21].…”

“…However, it is one of the innermost consequences of the laws of quantum mechanics that nonorthogonal states cannot be discriminated with certainty. Optimal detection strategies were first investigated by Helstrom [20,21] and Holevo [22] and a lot of attention has since been devoted to the development of optimal and near-optimal receivers for binary coherent states [23][24][25][26][27][28][29][30][31][32] and for the discrimination of larger signal alphabets [33][34][35][36][37][38][39][40][41]. An overview over different receiver schemes is provided in Appendix B.…”

Implementation of generalized quantum measurements for unambiguous discrimination of multiple non-orthogonal coherent states

“…Thus, real-world USD becomes an intermediate measurement strategy between MED and ideal USD, which retains the conclusive results of ideal USD, but contains some errors in those conclusive results. Although there do exist post-selectionbased conventional measurement techniques for coherent states characterized by errors and inconclusive results, they cannot improve upon standard-quantum-limited performance 2,20,21 . Thus, the goal becomes to realize a USD measurement with realistic imperfect devices that does surpass this conventional measurement limit.…”